Admittance

The impedance, , is composed of real and imaginary parts, Z = R + jX \,, where • is the resistance (ohms); and • is the reactance (ohms). Y = Z^{-1}= \frac{1}{R + jX} = \left( \frac{1}{R^2 + X^2} \right) \left(R - jX\right) Admittance, just like impedance, is a complex number, made up of a real part (the conductance, ), and an imaginary part (the susceptance, ), thus: Y = G + jB \,, where (conductance) and (susceptance) are given by: \begin{align} G &= \mathrm{Re}(Y) = \frac{R}{R^2 + X^2}\,, \\ B &= \mathrm{Im}(Y) = -\frac{X}{R^2 + X^2}\,. \end{align} The magnitude and phase of the admittance are given by: \begin{align} \left | Y \right | &= \sqrt{G^2 + B^2} = \frac{1}{\sqrt{R^2 + X^2}} \\ \angle Y &= \arctan \left( \frac{B}{G} \right) = \arctan \left( -\frac{X}{R} \right)\,, \end{align} where • is the conductance, measured in siemens; and • is the susceptance, also measured in siemens. Note that (as shown above) the signs of reactances become reversed in the admittance domain; i.e. capacitive susceptance is positive and inductive susceptance is negative. == Shunt admittance in electrical power systems modeling ==

In the context of electrical modeling of transformers and transmission lines, shunt components that provide paths of least resistance in certain models are generally specified in terms of their admittance. Each side of most transformer models contains shunt components which model magnetizing current and core losses. These shunt components can be referenced to the primary or secondary side. For simplified transformer analysis, admittance from shunt elements can be neglected. When shunt components have non-negligible effects on system operation, the shunt admittance must be considered. In the diagram below, all shunt admittances are referred to the primary side. The real and imaginary components of the shunt admittance, conductance and susceptance, are represented by and , respectively. Transmission lines can span hundreds of kilometers, over which the line's capacitance can affect voltage levels. For short length transmission line analysis, which applies to lines shorter than , this capacitance can be ignored and shunt components are not necessary in the model. Lines from , generally considered to be in the medium-line category, contain a shunt admittance governed by Y=yl=j\omega Cl\,, where • is the total shunt admittance; • is the shunt admittance per unit length; • is the length of the transmission line; and • is the capacitance of the line. ==See also==